Answer:
2926cm
Step-by-step explanation:
I hope it hepls you
F(x) sine curve with points at 0, 0 and pi over 2, 4 and pi, 0 and 3 pi over 2, negative 4 and 2 pi,0
g(x) x y 0 0 pi over 2 2 π 0 3 pi over 2 −2 2π 0
h(x) = 2 sin x + 3 Which function has the greatest rate of change on the interval from x = 0 to x = pi over 2
The change of f(x) from 0 to π/2 is 4
The change of g(x) from 0 to π/2 is 2
We can rule out g(x).
As for h(x):
h(0) = 2 sin(0) + 3 = 3
h(π/2) = 2(sin(π/2)) + 3 = 2 + 3 = 5
Change of h(x) from 0 to π/2 is 2.
Greatest change between 0 and π/2 is found with f(x)
Answer:
a) 
b) 
c)
![Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242](https://tex.z-dn.net/?f=Var%28X%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2%3D%20%5Cfrac%7B1%7D%7B2%7D%28e%5E2%20-1%29%20-%28e-1%29%5E2%20%3D%200.242)
Step-by-step explanation:
a) what must the value of C be so that f(x) is a probability density function?
In order to be a probability function we need this condition:

And solving the left part of the integral we have:

, so then 
b) find P(X<2)
We can find this probability on this way using the density function:

c) find E(X) and Var(X)
We can find the expected value on this way:
In order to find the Var(X) we need to find the second moment given by:
And now we can use the following definition:
![Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242](https://tex.z-dn.net/?f=Var%28X%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2%3D%20%5Cfrac%7B1%7D%7B2%7D%28e%5E2%20-1%29%20-%28e-1%29%5E2%20%3D%200.242)
the surface area of the cylinder is 0.5mm